-th moment

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-th moment

$\includegraphics[height=10mm]{images/moment}% WIDTH=48 HEIGHT=45$

The operator can be placed on the canvas in two ways:

From the Statistics (``statistics'') toolbar $\resizebox{!}{2ex}{\includegraphics{images/mean}}% WIDTH=15 HEIGHT=14$ ; or
By typing the letters ``moment'' on the canvas and then pressing the Enter key

Returns the $k$% WIDTH=16 HEIGHT=24

-th moment about the mean along a named dimension of all elements present. $k$% WIDTH=16 HEIGHT=24

is specified by the numerical argument of the operation, which defaults to 1 (hence the result will be 0 in that case). If the dimension is not named, then the $k$% WIDTH=16 HEIGHT=24

-th moment is over all elements present in the tensor. Note that missing elements are not counted.

$\begin{displaymath} \langle\Delta x^{k}\rangle=\frac{1}{N}\sum_{i}(x_{i}-\langle x\rangle)^{k} \end{displaymath}% WIDTH=377 HEIGHT=85$

Also $\begin{displaymath} \sigma^{2}=\frac{N}{N-1}\langle\Delta x^{2}\rangle \end{displaymath}% WIDTH=259 HEIGHT=68$